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Vacuum Science for Optics

Vacuum fundamentals for photonics — pressure regimes, gas kinetics, pumping systems, outgassing, and vacuum-compatible optical design.

Comprehensive Guide

1Introduction to Vacuum in Photonics

1.1Definition and Vacuum Ranges

Vacuum, from the Latin vacuus meaning empty, refers to any environment in which the gas pressure is significantly below standard atmospheric pressure. Standard atmospheric pressure at sea level is 101,325 Pa (760 Torr, 1013 mbar). Any pressure below this threshold constitutes a vacuum, though the practical significance of vacuum in photonics depends heavily on the degree of gas removal achieved.

Vacuum technology classifies pressure environments into several distinct ranges, each characterized by fundamentally different gas behavior. The boundaries between these ranges are not arbitrary — they correspond to transitions in molecular dynamics that determine whether gas-phase interactions affect optical performance.

RangePressure (Pa)Pressure (Torr)Molecular Density (cm⁻³)Mean Free PathMonolayer Time
Atmospheric1.01 × 10⁵7602.5 × 10¹⁹68 nm~3 ns
Low (rough)10⁵ – 10²760 – 0.7510¹⁹ – 10¹⁶68 nm – 67 μm3 ns – 3.5 μs
Medium10² – 10⁻¹0.75 – 7.5 × 10⁻⁴10¹⁶ – 10¹³67 μm – 67 mm3.5 μs – 3.5 ms
High (HV)10⁻¹ – 10⁻⁵7.5 × 10⁻⁴ – 7.5 × 10⁻⁸10¹³ – 10⁹67 mm – 670 km3.5 ms – 10 h
Ultra-high (UHV)10⁻⁵ – 10⁻¹⁰7.5 × 10⁻⁸ – 7.5 × 10⁻¹³10⁹ – 10⁴670 km – 6.7 × 10⁷ km10 h – 110 yr
Extreme high (XHV)< 10⁻¹⁰< 7.5 × 10⁻¹³< 10⁴> 10⁷ km> 110 yr
Table 1.1 — Vacuum Ranges and Properties (Air at 295 K)

At atmospheric pressure, molecules are separated by only a few nanometers and collide with each other after traveling roughly 68 nm — far shorter than the wavelength of visible light. In the high vacuum range, the mean free path exceeds the dimensions of typical vacuum chambers, meaning molecules travel from wall to wall without intermolecular collisions. This transition from gas-dominated to surface-dominated behavior is the defining physical characteristic that separates low vacuum from high vacuum, and it profoundly affects how optical systems perform inside vacuum enclosures.

Vacuum Pressure Rangesviscous → molecularLow / RoughMediumHighUHV10⁵10³10¹10⁻¹10⁻³10⁻⁵10⁻⁷10⁻¹⁰Pressure (Pa)Drying / PackagingSputteringE-beam / MBE
Figure 1.1 — Vacuum pressure ranges mapped against photonics applications. The transition from viscous to molecular flow occurs in the medium vacuum range.

1.2Why Optics Needs Vacuum

Vacuum environments serve four critical functions in photonic systems, each tied to a different aspect of light-matter interaction.

Contamination prevention. Molecular contamination is the primary reason most optical systems require vacuum. At atmospheric pressure, a clean surface acquires a complete monolayer of adsorbed gas molecules in roughly 3 nanoseconds. In high vacuum (10⁻⁴ Pa), that same monolayer takes seconds to form. For optical coating deposition — where film thickness must be controlled to fractions of a wavelength — even a partial monolayer of contaminant between deposited layers degrades reflectance, transmittance, and adhesion. Hydrocarbon contamination is particularly damaging in UV and VUV systems: absorbed UV photons crack hydrocarbon molecules into reactive fragments that polymerize on optical surfaces, producing permanent carbon deposits that reduce throughput.

Beam propagation. Gases absorb and scatter light. In the vacuum ultraviolet (VUV, λ < 200 nm) and extreme ultraviolet (EUV, λ < 30 nm) spectral regions, atmospheric gases — especially O₂ and H₂O — are strongly absorbing. EUV lithography, synchrotron beamlines, and VUV spectroscopy all require high vacuum or better to allow photon propagation over useful distances. Even in the visible and near-IR, turbulent density gradients in air cause beam wander and wavefront distortion. Interferometric measurements at the nanometer level — such as LIGO's gravitational wave detection — demand ultra-high vacuum to eliminate refractive index fluctuations along the beam path.

Process environment. Physical vapor deposition (PVD) processes — thermal evaporation, electron-beam evaporation, and sputtering — require vacuum to establish the mean free path necessary for deposited atoms to travel from source to substrate without scattering. Typical optical coating pressures range from 10⁻⁴ to 10⁻² Pa for evaporation and 0.1 to 1 Pa for sputtering. The vacuum level directly controls the microstructure, stress, and optical properties of deposited films.

Isolated environments. Many precision optical experiments require eliminating convective heat transfer, acoustic coupling, and gas-phase chemical reactions. Cold-atom experiments (magneto-optical traps, Bose-Einstein condensates) operate at UHV pressures below 10⁻⁸ Pa to achieve trap lifetimes of seconds to minutes — any collision between a room-temperature gas molecule and a micro-Kelvin atom ejects the atom from the trap. Ion trap quantum computing requires similar vacuum levels to minimize decoherence from background gas collisions.

Molecular Density ComparisonAtmosphere~2.5 × 10¹⁹ /cm³λ ≈ 68 nmHigh Vacuum~10¹⁰ /cm³λ ≈ 50 mUHV~10⁶ /cm³λ ≈ 500 km
Figure 1.2 — Molecular density and trajectories at three vacuum levels. Left: atmosphere (crowded). Center: high vacuum (wall-to-wall paths). Right: UHV (nearly empty).

2Pressure Units and Measurement

2.1Pressure Units

Vacuum technology uses a variety of pressure units — a consequence of the field's development across different national traditions and application domains. The SI unit of pressure is the pascal (Pa), defined as one newton per square meter. In practice, the pascal is inconveniently small for many vacuum applications: atmospheric pressure is 101,325 Pa, making even rough vacuum pressures unwieldy numbers. This has preserved the use of several non-SI units that remain deeply embedded in vacuum practice.

The torr, named after Evangelista Torricelli, is defined as exactly 1/760 of a standard atmosphere. It is nearly identical to the millimeter of mercury (mmHg), though the two are not formally equivalent because mmHg depends on local gravity and mercury density. The torr remains the dominant pressure unit in North American vacuum practice, particularly in semiconductor and optical coating industries. The millibar (mbar), equal to 100 Pa, is widely used in European vacuum practice and meteorology. For ultra-high vacuum work, the convention is to express pressures in Torr or mbar with scientific notation (e.g., 2 × 10⁻¹⁰ Torr).

Pressure definition
p=FAp = \frac{F}{A}
UnitPaTorrmbaratmpsi
1 Pa17.501 × 10⁻³1.000 × 10⁻²9.869 × 10⁻⁶1.450 × 10⁻⁴
1 Torr133.311.3331.316 × 10⁻³1.934 × 10⁻²
1 mbar100.07.501 × 10⁻¹19.869 × 10⁻⁴1.450 × 10⁻²
1 atm1.013 × 10⁵760.01013114.70
1 psi689551.7168.956.805 × 10⁻²1
Table 2.1 — Pressure Unit Conversion

Two particularly useful conversion factors for daily vacuum work: 1 Torr ≈ 4/3 mbar (exactly 1.33322 mbar), and 1 atm = 760 Torr = 1013.25 mbar = 101,325 Pa. The micron (μ or mTorr), equal to 10⁻³ Torr, appears in older literature and some industrial gauges.

🔧 Open Vacuum Pressure Converter

2.2Vacuum Gauges

No single gauge technology spans the full vacuum range from atmospheric pressure to ultra-high vacuum. Practical vacuum systems use multiple gauges, each covering a portion of the pressure spectrum, often combined into a single multi-gauge controller.

Mechanical gauges measure pressure through the physical deflection of a sensing element. Bourdon tubes and capsule gauges cover atmospheric to rough vacuum (10⁵ to ~10² Pa). They are gas-independent, robust, and require no electrical power, but lack the sensitivity for high vacuum measurement.

Capacitance diaphragm gauges (CDGs) measure the deflection of a thin metal diaphragm by sensing the capacitance between the diaphragm and a fixed electrode. They provide absolute, gas-independent pressure readings and cover roughly 5 decades of pressure per gauge head (e.g., 10⁻² to 10³ Pa for a 1000-Torr head). CDGs are the preferred gauge for process control in optical coating systems because their readings are unaffected by gas composition — critical during reactive deposition processes where the gas mixture changes continuously.

Thermal conductivity gauges (Pirani, thermocouple, and convection-enhanced Pirani) exploit the pressure dependence of gas thermal conductivity. A heated wire or filament loses heat to the surrounding gas at a rate that depends on pressure. These gauges are inexpensive and cover the rough-to-medium vacuum range (10⁵ to ~10⁻¹ Pa), but their readings are gas-dependent and they cannot distinguish between different gas species.

Ionization gauges operate by ionizing gas molecules and measuring the resulting ion current, which is proportional to gas density and hence pressure. The hot-cathode (Bayard-Alpert) gauge uses a heated filament to emit electrons that ionize gas molecules; it covers roughly 10⁻¹ to 10⁻⁹ Pa and is the workhorse of high vacuum measurement. Cold-cathode (Penning) gauges use crossed electric and magnetic fields to sustain a discharge without a heated filament; they are more robust but less accurate and cover 10⁻¹ to 10⁻⁷ Pa. Both types are gas-dependent.

Residual gas analyzers (RGAs), based on quadrupole mass spectrometry, identify individual gas species and their partial pressures. In UHV systems, the total pressure is the sum of partial pressures from water, hydrogen, CO, CO₂, hydrocarbons, and other residual species. An RGA is indispensable for diagnosing vacuum problems: a water-dominated spectrum indicates inadequate bakeout, while hydrocarbon peaks suggest pump oil backstreaming or outgassing from polymeric seals.

Gauge TypePressure Range (Pa)Gas Dependent?AccuracyTypical Application
Bourdon/capsule10⁵ – 10²No±1–5%Rough vacuum monitoring
Capacitance diaphragm10⁻² – 10⁵No±0.25–1%Coating process control
Pirani (thermal)10⁵ – 10⁻¹Yes±10–30%Roughing line, foreline
Convection Pirani10⁵ – 10⁻²Yes±10–15%Wide-range rough vacuum
Bayard-Alpert (hot cathode)10⁻¹ – 10⁻⁹Yes±15–25%HV/UHV chambers
Penning (cold cathode)10⁻¹ – 10⁻⁷Yes±50%HV process monitoring
Spinning rotor10⁻¹ – 10⁻⁵Weak±2–5%Calibration, reference
RGA (mass spec)< 10⁻²Species-resolvedVariesUHV diagnostics, leak detection
Table 2.2 — Vacuum Gauge Comparison

3Kinetic Gas Theory

3.1Ideal Gas Law

The behavior of dilute gases in vacuum systems is well described by the ideal gas law, which relates pressure to molecular density and temperature. For vacuum calculations, the most useful form expresses pressure in terms of the number density of molecules rather than moles.

Ideal gas law (molecular form)
p=nkBTp = n k_B T

Where pp = pressure (Pa), nn = number density (molecules/m³), kB=1.380649×1023k_B = 1.380649 \times 10^{-23} J/K, and TT = temperature (K).

At room temperature (T = 295 K), the number density at atmospheric pressure is approximately 2.5 × 10²⁵ molecules/m³. At 10⁻⁶ Pa (high vacuum), the density drops to about 2.5 × 10¹⁴ molecules/m³ — a reduction by a factor of 10¹¹, yet still containing hundreds of billions of molecules per cubic meter.

The concept of throughput (also called gas flow rate) is fundamental to vacuum system design. Throughput Q is defined as the volume of gas passing a point per unit time, multiplied by the pressure at that point:

Throughput
Q=pS=pdVdtQ = p \cdot S = p \cdot \frac{dV}{dt}

Throughput is conserved along a pumping line at steady state: the same number of molecules per second passes every cross-section of the pipe, regardless of the local pressure. This principle — analogous to current conservation in an electrical circuit — is the basis for vacuum system analysis.

3.2Mean Free Path

The mean free path λ is the average distance a molecule travels between successive collisions with other molecules. It is the single most important parameter for characterizing gas behavior in a vacuum system, because its relationship to the system dimensions determines the flow regime and hence the choice of pumping, gauging, and system design strategies.

Mean free path
λ=kBT2πd2p\lambda = \frac{k_B T}{\sqrt{2}\, \pi\, d^2\, p}

Where dd = effective molecular diameter (m). For nitrogen (d3.7×1010d \approx 3.7 \times 10^{-10} m) or air at room temperature (T = 295 K), this simplifies to:

Mean free path for air at room temperature
λair6.6×103p(m, with p in Pa)\lambda_{\text{air}} \approx \frac{6.6 \times 10^{-3}}{p} \quad \text{(m, with } p \text{ in Pa)}
🔧 Open Mean Free Path Calculator
Worked Example: Mean Free Path at High Vacuum

Problem: Calculate the mean free path of nitrogen molecules at a pressure of 1.33 × 10⁻⁴ Pa (10⁻⁶ Torr) and temperature 295 K. The effective diameter of N₂ is 3.7 × 10⁻¹⁰ m.

Step 1: Substitute into the mean free path equation:

λ = k_BT / (√2 · π · d² · p)
λ = (1.381 × 10⁻²³)(295) / (√2 · π · (3.7 × 10⁻¹⁰)² × 1.33 × 10⁻⁴)

Step 2: Evaluate numerator and denominator:

k_BT = 4.074 × 10⁻²¹ J
√2·π·d² = 6.08 × 10⁻¹⁹ m²
Denominator = 6.08 × 10⁻¹⁹ × 1.33 × 10⁻⁴ = 8.09 × 10⁻²³ Pa·m²

Step 3: Divide:

λ ≈ 50.4 m

Interpretation: At 10⁻⁶ Torr, gas molecules travel approximately 50 meters between collisions — far exceeding the dimensions of any laboratory vacuum chamber. Molecules interact almost exclusively with the chamber walls, not with each other. This is the molecular flow regime.

3.3Molecular Impingement Rate and Monolayer Formation Time

The impingement rate — the number of gas molecules striking a surface per unit area per unit time — determines how quickly a clean surface becomes contaminated. This is a critical consideration for optical coating deposition, surface science, and any application where surface cleanliness affects performance.

Molecular impingement rate (Hertz-Knudsen equation)
Φ=nvˉ4=p2πmkBT\Phi = \frac{n \bar{v}}{4} = \frac{p}{\sqrt{2 \pi m k_B T}}

The monolayer formation time τ_ML is the time required for a freshly created, perfectly clean surface to be covered by a complete monolayer of adsorbed gas molecules, assuming a sticking coefficient of unity:

Monolayer formation time
τML=nsΦ\tau_{ML} = \frac{n_s}{\Phi}

Where ns1019n_s \approx 10^{19} molecules/m² (typical surface site density). For air at room temperature:

τML3.5×104p(s, with p in Pa)\tau_{ML} \approx \frac{3.5 \times 10^{-4}}{p} \quad \text{(s, with } p \text{ in Pa)}
Worked Example: Monolayer Formation Time at HV vs. UHV

Problem: Compare the monolayer formation time for a clean surface at (a) high vacuum, p = 10⁻⁴ Pa, and (b) ultra-high vacuum, p = 10⁻⁸ Pa. Assume air at 295 K.

At HV (p = 10⁻⁴ Pa):

τ_ML = 3.5 × 10⁻⁴ / 10⁻⁴ = 3.5 s

At UHV (p = 10⁻⁸ Pa):

τ_ML = 3.5 × 10⁻⁴ / 10⁻⁸ = 3.5 × 10⁴ s ≈ 9.7 hours

Interpretation: At high vacuum, a clean surface accumulates a monolayer of contamination in a few seconds — adequate for optical coating processes where deposition rates of nm/s easily outpace contamination, but marginal for precision surface science. At ultra-high vacuum, the surface remains pristine for nearly half a day, enabling the study of atomically clean surfaces and the growth of ultra-pure thin films. This explains why surface science and advanced coating techniques require UHV conditions.

The Langmuir (L) is a convenient unit of gas exposure used in surface science: 1 L = 10⁻⁶ Torr·s = 1.33 × 10⁻⁴ Pa·s. An exposure of 1 L corresponds roughly to the dose needed to form one monolayer (assuming unit sticking coefficient), although the actual sticking coefficient is typically much less than unity for most gas-surface combinations at room temperature.

4Gas Flow Regimes

4.1Knudsen Number

The behavior of gas flow through a vacuum system depends on the relationship between the mean free path λ and the characteristic dimension D of the flow channel (typically the pipe diameter). This relationship is quantified by the Knudsen number:

Knudsen number
Kn=λD\text{Kn} = \frac{\lambda}{D}
Knudsen NumberFlow RegimeBehavior
Kn < 0.01Viscous (continuum)Molecule-molecule collisions dominate; gas behaves as a fluid
0.01 < Kn < 0.5Transitional (Knudsen)Both intermolecular and wall collisions are significant
Kn > 0.5MolecularMolecule-wall collisions dominate; molecules travel independently
Table 4.1 — Flow Regime Classification

For a 5 cm diameter pipe and air at room temperature, the transition to molecular flow occurs at approximately 0.13 Pa (10⁻³ Torr), which falls in the medium vacuum range. This means that most high vacuum and ultra-high vacuum systems operate entirely in the molecular flow regime, while rough pumping proceeds through viscous and transitional flow.

4.2Viscous Flow

At pressures where Kn < 0.01, gas flows as a continuum fluid. Two sub-regimes exist: laminar (smooth, layered flow) and turbulent (chaotic, mixing flow), distinguished by the Reynolds number. In vacuum systems, viscous flow is typically laminar. The throughput for laminar viscous flow through a cylindrical tube is described by the Poiseuille equation:

Poiseuille flow (viscous, laminar)
Qvisc=πD4128ηL(p12p22)2Q_{\text{visc}} = \frac{\pi D^4}{128 \eta L} \cdot \frac{(p_1^2 - p_2^2)}{2}

Where η\eta = dynamic viscosity (for air at 295 K, η ≈ 1.84 × 10⁻⁵ Pa·s). The conductance in viscous flow is pressure-dependent: it increases with the mean pressure in the tube because more molecules are available to participate in the collective fluid flow.

4.3Molecular Flow

At pressures where Kn > 0.5, molecules move independently, colliding only with the walls. The conductance in molecular flow depends only on geometry and gas species, not on pressure.

Molecular flow conductance of a thin orifice
Corifice=AkBT2πm=Avˉ4C_{\text{orifice}} = A \sqrt{\frac{k_B T}{2 \pi m}} = A \cdot \frac{\bar{v}}{4}

For air at 20°C, this evaluates to approximately 11.6 L/(s·cm²) of orifice area.

Molecular flow conductance of a long cylindrical tube
Ctube=πD312LkBT2πmC_{\text{tube}} = \frac{\pi D^3}{12 L} \sqrt{\frac{k_B T}{2 \pi m}}

For air at 20°C, the engineering form is:

Ctube12.1D3L(L/s, with D,L in cm)C_{\text{tube}} \approx 12.1 \frac{D^3}{L} \quad \text{(L/s, with } D, L \text{ in cm)}

The strong cubic dependence on diameter means that doubling the pipe diameter increases molecular flow conductance by a factor of eight. This is the single most important rule in vacuum system plumbing: maximize diameter, minimize length.

Conductances in series and parallel follow rules analogous to resistors in electrical circuits:

Series conductance
1Ctotal=1C1+1C2++1Cn\frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} + \cdots + \frac{1}{C_n}
Parallel conductance
Ctotal=C1+C2++CnC_{\text{total}} = C_1 + C_2 + \cdots + C_n
Worked Example: Conductance of a Cylindrical Tube in Molecular Flow

Problem: Calculate the molecular flow conductance for air at 20°C through a stainless steel tube with inner diameter 10 cm and length 50 cm.

Step 1: Apply the long-tube engineering formula:

C_long = 12.1 × D³/L = 12.1 × (10)³/50 = 12.1 × 20 = 242 L/s

Step 2: Clausing factor for L/D = 5: K ≈ 0.31

Step 3: Apply correction:

C_eff = K × C_long = 0.31 × 242 = 75 L/s

Interpretation: The Clausing correction reduces the conductance by roughly a factor of 3 for this moderate L/D ratio. A 500 L/s turbomolecular pump connected through this tube delivers an effective pumping speed of only 1/(1/500 + 1/75) ≈ 65 L/s at the chamber — the tube is the limiting element.

Gas Flow RegimesViscous LaminarKn < 0.01parabolic profileTransitional0.01 < Kn < 0.5mixed collisionsMolecularKn > 0.5wall-to-wall pathsincreasing vacuum (decreasing pressure) →
Figure 4.1 — Gas flow regimes through a pipe. Left: viscous laminar flow with parabolic velocity profile. Center: transitional flow. Right: molecular flow with independent wall-to-wall trajectories.

5Vacuum Pumps

5.1Positive Displacement Pumps

Positive displacement pumps mechanically capture a volume of gas, compress it, and expel it to atmosphere (or to the exhaust of another pump). They are the workhorses of rough pumping, bringing chambers from atmosphere to pressures where high vacuum pumps can take over.

Rotary vane pumps use an eccentrically mounted rotor with spring-loaded vanes that sweep gas from the inlet to the exhaust. Oil-sealed versions achieve ultimate pressures of ~1 Pa (10⁻² mbar) in single-stage and ~10⁻¹ Pa in two-stage configurations. Their primary drawback is oil backstreaming: oil vapor can migrate into the vacuum chamber, contaminating optical surfaces.

Scroll pumps use two interleaving spiral scrolls — one fixed, one orbiting — to compress gas without oil in the pumping volume. They achieve ultimate pressures around 1 Pa and are widely used as clean backing pumps for turbomolecular pumps in optical applications.

Diaphragm pumps use a reciprocating diaphragm to displace gas. They are entirely oil-free, achieve ultimate pressures around 200–500 Pa, and serve as clean rough pumps for small systems.

Roots (booster) pumps use two counter-rotating lobed rotors to displace large gas volumes at low compression ratios. They cannot operate alone against atmospheric pressure and require a backing pump. Roots-backed-by-scroll or Roots-backed-by-rotary-vane combinations provide high pumping speeds (hundreds to thousands of L/s) through the medium vacuum range.

5.2Momentum Transfer Pumps

Turbomolecular pumps (TMPs) are the dominant high vacuum pump in optical and photonic applications. Multiple stages of angled rotor blades, spinning at 20,000–90,000 RPM, collide with gas molecules and impart momentum toward the exhaust. Modern TMPs achieve ultimate pressures below 10⁻⁸ Pa with pumping speeds from tens to thousands of liters per second. They offer several advantages critical for optics: oil-free operation, high pumping speed for all gases, fast startup, and high compression ratios for heavy molecules. Magnetic-bearing versions produce minimal vibration, making them suitable for interferometry and precision optical measurement.

Diffusion pumps use jets of heated oil or silicone-based fluid to entrain gas molecules. They achieve ultimate pressures of 10⁻⁷ to 10⁻⁸ Pa with very high pumping speeds at relatively low cost. Their principal disadvantage is oil backstreaming.

5.3Entrapment Pumps

Cryopumps condense gas molecules onto surfaces cooled to 10–20 K by a closed-cycle helium cryocooler. They achieve ultimate pressures below 10⁻⁸ Pa and offer extremely high pumping speeds for water vapor. Cryopumps require periodic regeneration — warming to release accumulated gas.

Ion pumps (sputter ion pumps) ionize gas molecules, accelerate the resulting ions into a titanium cathode, and bury them by sputtering fresh titanium over them. They are vibration-free, oil-free, and achieve ultimate pressures below 10⁻⁹ Pa. Ion pumps are standard in UHV systems for surface science, cold-atom experiments, and precision interferometry.

Getter pumps (non-evaporable getters, NEGs, and titanium sublimation pumps, TSPs) use chemically active metals to bind reactive gases (H₂, H₂O, CO, CO₂, O₂, N₂). NEG strips can be activated by heating and provide distributed pumping inside narrow-geometry chambers. Neither type pumps noble gases or methane.

5.4Pump Selection for Optics

Pump TypePressure Range (Pa)Speed (L/s)Oil-Free?Best For
Rotary vane10⁵ – 11–100NoIndustrial rough pumping
Scroll10⁵ – 15–50YesClean backing for TMPs
Diaphragm10⁵ – 2000.5–5YesSmall clean systems
Roots + backing10⁵ – 10⁻¹100–5000DependsLarge chamber pumpdown
Turbomolecular10⁻¹ – 10⁻⁸50–5000YesGeneral HV/UHV, precision optics
Diffusion10⁻¹ – 10⁻⁷100–50000NoLarge coating systems
Cryopump10⁻¹ – 10⁻⁸500–10000YesWater pumping, coating systems
Ion pump10⁻⁴ – 10⁻⁹2–500YesUHV, vibration-free systems
TSP/NEG10⁻⁵ – 10⁻¹⁰100–5000YesSupplementary UHV pumping
Table 5.1 — Pump Type Comparison for Optical Applications

For a precision optical coating system, a typical pump configuration consists of a dry scroll pump backing a turbomolecular pump, achieving base pressures of 10⁻⁵ to 10⁻⁶ Pa without oil contamination. For UHV surface science or cold-atom systems, a turbo-pumped system is baked to remove water, then maintained by an ion pump for vibration-free, maintenance-free operation in the 10⁻⁸ to 10⁻⁹ Pa range.

Vacuum Pump Operating RangesPositive DisplacementDiaphragmScrollRotary VaneMomentum TransferTurbomolecularDiffusionEntrapmentCryopumpIon PumpTi Sublimation10-1010-5100105Pressure (Pa)
Figure 5.1 — Pump coverage map showing operating pressure ranges for each pump type. Blue = positive displacement, copper = momentum transfer, green = entrapment.

6Outgassing and Gas Loads

6.1Outgassing Sources

In a well-sealed vacuum system free from leaks, the ultimate pressure is determined by the balance between gas input from internal sources and the system's pumping speed. The dominant internal gas source is outgassing: the release of gas molecules from the surfaces and bulk of materials inside the vacuum chamber.

Desorption is the release of molecules adsorbed on surfaces. Water vapor is the primary desorbate in unbaked vacuum systems: several monolayers of H₂O are always present on surfaces exposed to atmospheric air. The water desorption rate decreases roughly as 1/t, where t is the pumping time, which is why pumpdown curves exhibit a characteristic slow approach to base pressure after the initial rapid evacuation.

Diffusion is the release of gas dissolved within the bulk of a material. Hydrogen is the dominant diffusant in stainless steel — it dissolves in the metal during manufacturing and slowly migrates to the surface under vacuum. Bulk hydrogen outgassing ultimately limits the base pressure of unbaked stainless steel systems to the 10⁻⁵ to 10⁻⁶ Pa range.

Permeation is the steady-state transport of gas through a material driven by a pressure gradient across the wall. Helium permeation through glass and quartz is the classic example. Elastomeric seals (O-rings) are permeable to all atmospheric gases; their permeation rate limits the ultimate pressure of O-ring-sealed systems to the high vacuum range.

6.2Outgassing Rates

MaterialConditionq (Pa·m/s)Dominant Species
304L stainless steelAs received, 24 h pump~10⁻⁶H₂O
304L stainless steel150°C bake, 24 h~10⁻⁸H₂
304L stainless steel950°C vacuum fire + 150°C bake~10⁻¹⁰H₂
316L stainless steelAs received, 24 h pump~10⁻⁶H₂O
Aluminum (6061)As received, 24 h pump~10⁻⁶H₂O
Aluminum (6061)150°C bake~10⁻⁸H₂
OFHC copperBaked~10⁻⁹H₂
Viton (FKM) O-ring24 h pump~10⁻⁵H₂O, organics
PTFE (Teflon)24 h pump~10⁻⁶H₂O
Borosilicate glass24 h pump~10⁻⁶H₂O, He (permeation)
Fused silica24 h pump~10⁻⁷H₂O
Table 6.1 — Typical Outgassing Rates

These values span five orders of magnitude, emphasizing that material selection profoundly affects achievable vacuum levels. For UHV systems, the rule is straightforward: use baked stainless steel with metal seals, and minimize the use of polymeric materials.

6.3Bakeout

Baking a vacuum system — heating it to an elevated temperature under vacuum — dramatically accelerates the removal of adsorbed water and dissolved gases. A 150°C bake for 24–48 hours typically reduces water outgassing by two to three orders of magnitude, dropping the base pressure from the 10⁻⁵ Pa range to 10⁻⁷ or 10⁻⁸ Pa.

Outgassing rate temperature dependence
q=q0exp ⁣(Ea2kBT)q = q_0 \exp\!\left(-\frac{E_a}{2 k_B T}\right)

The activation energy for water desorption from stainless steel is approximately 0.9–1.0 eV, while hydrogen diffusion from the bulk has E_a ≈ 0.5 eV.

Practical bakeout guidelines for optical vacuum systems: use only vacuum-compatible heaters; ramp temperature slowly (1–2°C/min) to avoid thermal stress on viewports and seals; maintain bake temperature for at least 24 hours; cool slowly before turning off ion gauges and closing valves; verify that the base pressure after bake is at least 10× lower than before.

6.4NASA/ASTM E595

For space, semiconductor, and precision optical applications, materials are screened for outgassing potential using the ASTM E595 test method. A sample is heated to 125°C in vacuum for 24 hours, and two quantities are measured:

Total Mass Loss (TML): the percentage of mass lost from the sample. Collected Volatile Condensable Materials (CVCM): the percentage of mass that condenses on a collector plate at 25°C. Materials are considered low-outgassing if TML < 1.0% and CVCM < 0.10%. NASA maintains a searchable database of tested materials. When selecting adhesives, coatings, lubricants, or polymeric components for vacuum-optical systems, specifying ASTM E595-qualified materials prevents contamination problems before they start.

7Vacuum System Design

7.1Chamber Materials and Flanges

Stainless steel (304L, 316L, 316LN) is the standard material for HV and UHV chambers. It is non-magnetic (in the austenitic condition), accepts welding and electropolishing, and can be baked to 450°C with metal seals. Electropolished or mechanically polished interior surfaces reduce the effective surface area and lower outgassing rates.

Aluminum alloys (6061-T6, 6063) offer lower cost, lower mass, and higher thermal conductivity than steel. They are non-magnetic and have low hydrogen outgassing. However, aluminum's lower bakeout temperature limit (~200°C) restricts its use in UHV. Aluminum is excellent for HV coating chambers and space instrument enclosures.

Flange TypeSealBakeout LimitPressure RangeTypical Use
KF (Klein Flange) / NWElastomer O-ring150°CHV (10⁻⁵ Pa)Rough lines, HV systems
ISO-K / ISO-FElastomer O-ring150°CHV (10⁻⁵ Pa)Large HV chambers
CF (ConFlat)Copper gasket (OFHC)450°CUHV (10⁻¹⁰ Pa)UHV/XHV, bakeable systems
WheelerIndium wireLow (~80°C)UHVCryogenic, optical viewports
Table 7.1 — Vacuum Flange and Seal Comparison

7.2Seals and Feedthroughs

Elastomer seals (Viton, EPDM, silicone, Kalrez) are convenient and reusable. Viton (fluoroelastomer, FKM) is the most common, with a bakeout limit of ~200°C and outgassing rates that limit base pressure to the 10⁻⁵ to 10⁻⁶ Pa range. Metal seals (copper, aluminum, indium, gold) enable bakeout to higher temperatures and achieve lower leak rates. Copper gaskets in CF flanges are the standard for UHV. Indium wire seals are used for cryogenic and fragile-substrate applications.

Feedthroughs provide electrical, optical, and mechanical access through the vacuum wall. Electrical feedthroughs use glass-to-metal or ceramic-to-metal seals. Optical feedthroughs (viewports) are windows brazed or sealed into flanges. Motion feedthroughs use bellows-sealed or magnetically coupled drives. All feedthroughs must be rated for the intended vacuum level and bakeout temperature.

7.3Pumping Speed and Effective Pumping Speed

The pumping speed S_p of a pump is the volume of gas it removes per unit time at its inlet. The effective pumping speed at the chamber is always less than S_p because the connecting tubes, valves, and baffles restrict gas flow.

Effective pumping speed
1Seff=1Sp+1C\frac{1}{S_{\text{eff}}} = \frac{1}{S_p} + \frac{1}{C}

This equation shows that S_eff is always less than both S_p and C. When C ≫ S_p, the pump is the limiting factor and S_eff ≈ S_p. When C ≪ S_p, the plumbing is the bottleneck and S_eff ≈ C.

Worked Example: Effective Pumping Speed Through a Tube and Valve

Problem: A 300 L/s turbomolecular pump is connected to a chamber through a 10 cm diameter, 30 cm long tube and a right-angle valve with a conductance of 150 L/s. What is the effective pumping speed at the chamber?

Step 1: Calculate tube conductance:

C_long = 12.1 × 10³/30 = 403 L/s
Clausing factor for L/D = 3: K ≈ 0.39
C_tube = 0.39 × 403 = 157 L/s

Step 2: Total conductance (series):

1/C_total = 1/157 + 1/150 = 0.01304
C_total = 76.7 L/s

Step 3: Effective pumping speed:

1/S_eff = 1/300 + 1/76.7 = 0.01637
S_eff ≈ 61 L/s

Interpretation: The 300 L/s pump delivers only 61 L/s at the chamber — an 80% reduction. The conductance-limited plumbing, not the pump, determines system performance.

7.4Pumpdown Estimation

Roughing pumpdown time
t=VSeffln ⁣(p1p2)t = \frac{V}{S_{\text{eff}}} \ln\!\left(\frac{p_1}{p_2}\right)
Ultimate base pressure
pbase=qASeffp_{\text{base}} = \frac{q \cdot A}{S_{\text{eff}}}
🔧 Open Pumpdown Estimator
Worked Example: Pumpdown Time and Base Pressure

Problem: A cylindrical vacuum chamber has diameter 40 cm and length 60 cm. It is pumped by a turbomolecular pump with S_eff = 100 L/s. Internal surface area is 1.2 m². Outgassing rate after 24 h is 5 × 10⁻⁷ Pa·m/s. (a) How long does roughing from atmosphere to 10 Pa take with a 10 L/s scroll pump? (b) What is the ultimate base pressure?

Step 1: Chamber volume:

V = π r²L = π(0.2)²(0.6) = 0.0754 m³ = 75.4 L

Step 2: Roughing time (atmosphere to 10 Pa):

t_rough = (75.4/10) × ln(101325/10)
= 7.54 × 9.22 = 69.5 s

Step 3: Ultimate base pressure:

p_base = (5 × 10⁻⁷ × 1.2) / 0.100
= 6.0 × 10⁻⁶ Pa (4.5 × 10⁻⁸ Torr)

Interpretation: Roughing takes ~70 seconds. The base pressure of 6 × 10⁻⁶ Pa is limited by outgassing. A 150°C bakeout (reducing q to ~5 × 10⁻⁹ Pa·m/s) would lower the base pressure to ~6 × 10⁻⁸ Pa (UHV range).

Optical Vacuum SystemChamberViewportIon GaugeLeak Valvegas inletVentGate ValveTurbo PumpPiraniforelineRoughing Pumpexhaust →
Figure 7.1 — Schematic of a typical optical vacuum system showing the pumping stack, gauging, and gas inlet.

8Vacuum-Compatible Optics and Hardware

8.1Vacuum Viewports and Windows

Optical viewports provide laser access, illumination, and imaging paths through the vacuum wall. The window material must satisfy transmission, vacuum compatibility, and mechanical requirements simultaneously.

MaterialTransmission RangeMax Temp (°C)He PermeationTypical Application
Fused silica180 nm – 3.5 μm1000ModerateUV/Vis/NIR laser access
Borosilicate350 nm – 2.5 μm500LowGeneral-purpose viewing
Sapphire150 nm – 5.5 μm1800Very lowUV, high pressure, rugged
MgF₂115 nm – 7.5 μm700Very lowVUV spectroscopy
CaF₂130 nm – 10 μm600Very lowUV to mid-IR
ZnSe0.5 – 22 μm250Very lowCO₂ laser, thermal imaging
BaF₂150 nm – 12.5 μm500Very lowBroad IR, thermography
Germanium2 – 14 μm200Very lowThermal IR
CVD diamond225 nm – far IR>500Very lowHigh power, broad spectrum
Table 8.1 — Vacuum Window Materials

Fused silica is the default choice for UV/visible/NIR applications. For VUV work (λ < 200 nm), MgF₂ or CaF₂ windows are required. Anti-reflection coatings on viewports must be vacuum-compatible and survive bakeout temperatures.

Worked Example: Viewport Transmission at 193 nm

Problem: Compare the single-pass transmission of fused silica, MgF₂, and CaF₂ viewports (3 mm thick, uncoated) at 193 nm (ArF excimer).

Internal transmittance at 193 nm (3 mm):

UV-grade fused silica: ~88%
MgF₂: ~93%
CaF₂: ~95%

Fresnel losses (uncoated, both surfaces):

Fused silica (n ≈ 1.56): T_surfaces ≈ 90.6%
MgF₂ (n ≈ 1.43): T_surfaces ≈ 93.9%
CaF₂ (n ≈ 1.50): T_surfaces ≈ 92.2%

Total single-pass transmission:

CaF₂ ≈ 88%, MgF₂ ≈ 87%, Fused silica ≈ 80%

Interpretation: CaF₂ and MgF₂ both outperform fused silica at 193 nm. With AR coatings, CaF₂ viewports routinely achieve >93% transmission at 193 nm.

8.2Vacuum-Compatible Optomechanics

Venting. Trapped volumes (blind tapped holes, sealed cavities, enclosed air spaces) create virtual leaks: gas slowly escapes from the trapped volume into the vacuum, extending pumpdown times indefinitely. All screw holes must be vented (through-holes or vent grooves), and all enclosed volumes must have gas escape paths.

Material restrictions. Acceptable materials include stainless steel, aluminum, titanium, OFHC copper, Invar, and ceramics (Macor, alumina). Materials to avoid: zinc-plated hardware (outgasses zinc), cadmium-plated hardware (toxic outgassing), brass (outgasses zinc), nylon and most plastics (high outgassing), standard greases and lubricants.

Lubricants. Conventional grease-based lubricants are unacceptable in vacuum. Vacuum-compatible alternatives include dry-film lubricants (MoS₂, WS₂, PTFE-based), vacuum greases (Apiezon, Krytox), and solid lubricant coatings (silver, lead).

8.3Thermal Management in Vacuum

Without atmospheric convection, heat dissipation in vacuum relies entirely on conduction and radiation.

Radiative heat transfer (Stefan-Boltzmann)
Q˙=εσA(T14T24)\dot{Q} = \varepsilon \sigma A (T_1^4 - T_2^4)

Where ε = effective emissivity (0 to 1), σ = 5.67 × 10⁻⁸ W/(m²·K⁴), A = radiating area (m²), and T₁, T₂ = surface temperatures (K). Polished metal surfaces have low emissivity (ε ≈ 0.02–0.1), making them effective radiation shields. Motors and actuators inside vacuum chambers generate heat that cannot be removed by convection — stepper motors are commonly derated to 20–50% of atmospheric power rating.

CF Viewport AssemblySide Cross-SectionCF FlangeCu GasketKnife EdgeAR CoatingsFused SilicaGlass-Metal Brazevacuum side ↑Front Face ViewApertureBoltHolesGasket RingFlange OD
Figure 8.1 — Cross-section of a CF viewport showing knife-edge seal, copper gasket, fused silica window, AR coatings, and glass-to-metal braze.

9Optical Applications of Vacuum

9.1Thin Film Deposition

Vacuum is essential for all physical vapor deposition (PVD) processes because the deposited atoms must travel from source to substrate without excessive scattering. Thermal evaporation heats a source material until it evaporates at base pressures of 10⁻⁴ to 10⁻⁶ Pa. Electron-beam evaporation extends this to high-melting-point materials (SiO₂, TiO₂, Ta₂O₅) used in optical multilayer coatings.

Sputtering bombards a target with argon ions from a plasma at 0.1–1 Pa, producing denser films with better adhesion. Ion-beam sputtering (IBS) provides the highest-quality optical coatings for precision applications (total losses < 1 ppm). The vacuum environment during deposition directly affects film microstructure: higher base pressures incorporate more residual gas molecules into the film, increasing absorption and scatter losses.

9.2Laser Systems

Several laser technologies require vacuum for operation or beam delivery. Gas lasers that operate on transitions in noble gases (ArF, KrF, XeF excimer) require vacuum or inert gas purge for the optical path outside the laser cavity, particularly at VUV wavelengths. High-power laser systems can damage optics by laser-induced contamination (LIC) — hydrocarbon molecules adsorbed on surfaces decompose and deposit carbon. Operating high-power laser optics in vacuum eliminates this mechanism. VUV and EUV sources (free-electron lasers, synchrotrons, HHG sources) require HV to UHV for beam propagation.

9.3Spectroscopy and Beamlines

Synchrotron beamlines operate at 10⁻⁷ to 10⁻⁹ Pa to prevent beam scattering and optic contamination. Beamline optics — mirrors, gratings, crystals — are mounted on precision vacuum-compatible stages and are often water-cooled. Mass spectrometry requires vacuum in the 10⁻⁴ to 10⁻⁷ Pa range for ion beam formation and detection. Electron microscopy operates at similar pressures.

9.4Quantum Optics and Cold Atoms

Magneto-optical traps (MOTs) cool and trap neutral atoms using laser beams in UHV chambers at pressures below 10⁻⁸ Pa. Trap lifetime is inversely proportional to background pressure — achieving trap lifetimes of minutes to hours requires 10⁻⁹ to 10⁻¹⁰ Pa. Ion trap quantum computing requires similar vacuum levels. Both MOT and ion trap systems require 6–12 viewports while maintaining UHV integrity, creating a significant engineering challenge at the intersection of vacuum science and optical design.

10Vacuum System Selection Workflow

10.1Requirements Gathering

Designing a vacuum system for an optical application begins with defining the requirements. Target pressure: optical coating typically requires 10⁻⁴ to 10⁻⁶ Pa; surface science and cold atoms require 10⁻⁸ to 10⁻¹⁰ Pa. Gas species and cleanliness: is hydrocarbon-free vacuum required? Optical access: how many viewports, at what wavelengths and clear aperture? Size and geometry: what is the working volume? Duty cycle: is the system pumped continuously or vented frequently?

10.2System Sizing

Once requirements are defined, the system is sized through a systematic process: (1) estimate the gas load from outgassing (surface area × outgassing rate) and any process gas flow; (2) calculate the required pumping speed from S_eff = Q_total / p_target; (3) select the pump with S_p > S_eff, accounting for conductance losses; (4) design the plumbing to maximize conductance (short, wide tubes; minimize bends); (5) verify pumpdown time meets operational requirements; (6) select gauging to cover the full pressure range from atmosphere to base pressure.

10.3Common Pitfalls

Virtual leaks. Trapped gas in blind tapped holes, unsealed cavities, or double O-ring grooves slowly releases into the vacuum, producing symptoms identical to a real leak but with no external leak source. Always vent all fastener holes and avoid trapped volumes.

Wrong seal material. Using Viton O-rings in a system that requires UHV guarantees failure — elastomer outgassing prevents reaching pressures below ~10⁻⁵ Pa regardless of pump size. Conversely, using CF flanges on a system that only needs rough vacuum adds unnecessary cost.

Inadequate bakeout. Failing to bake a UHV system after every vent to atmosphere means that water outgassing dominates the pressure indefinitely. A 24-hour bake at 150°C is essential after every air exposure.

Pump-limited vs. conductance-limited. Many systems underperform because the plumbing restricts gas flow, not because the pump is too small. Always calculate the effective pumping speed at the chamber, not just the pump specification.

Contamination from handling. Fingerprints deposit approximately 10⁻⁵ g/cm² of hydrocarbon contamination. All vacuum components should be handled with clean gloves and cleaned with appropriate solvents (acetone, then methanol or isopropanol) before assembly.

References

  1. [1]J. F. O'Hanlon, A User's Guide to Vacuum Technology, 3rd ed. Wiley, 2003.
  2. [2]K. Jousten (ed.), Handbook of Vacuum Technology, 2nd ed. Wiley-VCH, 2016.
  3. [3]A. Chambers, Modern Vacuum Physics, 2nd ed. CRC Press, 2017.
  4. [4]P. A. Redhead, J. P. Hobson, and E. V. Kornelsen, The Physical Basis of Ultrahigh Vacuum. AIP, 1993.
  5. [5]ASTM E595-15, Standard Test Method for Total Mass Loss and Collected Volatile Condensable Materials from Outgassing in a Vacuum Environment. ASTM International, 2021.
  6. [6]D. M. Mattox, Handbook of Physical Vapor Deposition Processing, 2nd ed. Elsevier, 2010.
  7. [7]Pfeiffer Vacuum, The Vacuum Technology Book, Vol. II. Pfeiffer Vacuum GmbH, 2013.
  8. [8]E. Al-Dmour, “Fundamentals of Vacuum Physics and Technology,” in Proc. CERN Accelerator School: Vacuum for Particle Accelerators (Glumslöv, Sweden), CERN-2020-009, 2020.

All information, equations, and calculations have been compiled and verified to the best of our ability. For mission-critical applications, we recommend independent verification of all values. If you find an error, please let us know.